Do mirrors have fresnel?
Physically speaking - that means if we are talking about a 100% reflective material - I'd say no. 

In reality there is no material that has 100% reflectivity and of course it depends on the materials. If you have a highly polished chrome ball, the fresnel effect would be much lower than that of a normal glass mirror, that has only one side coated with aluminum, sliver or gold. 

But in any case, the reflections on a highly reflective surface would surpass every possible Fresnel effect to a point where you wouldn't notice it anymore.